This is not intended to be an exhaustive list, nor help you solve specific puzzles.
However, it will give you an idea of how to approach puzzles...
... and some of the techniques you are likely to encounter.

GENERAL

The puzzle title, where one exists, is normally there for a good reason. It may hint towards the method required to solve a puzzle; how to apply a method; or simply relate to the answer.

Similarly, everything contained within the puzzle is normally there for a reason, and it pays not to overlook seemingly innocent details. For example: if a puzzle comprised of five words, and those words were numbered 1-5, then there is a very good possibility that the numbers are needed.

The way in which a puzzle is laid out is also important. If a puzzle contains a number of objects ask yourself why they are laid out how they are. For example: if a puzzle contained, say, nine pictures but instead of being laid out as three rows of three, it has 3 pictures in the top row, 2 in the middle and 4 on the bottom then it probably represents a 3 word answer of the format 3,2,4.

Finally, if in doubt, check the source. It is not uncommon for a hint or clue to be hidden there!

PUZZLE TYPES

There are an infinite number of types of puzzle, and it would be impossible to cover them all. However, the following list is a summary of types which seem to turn up quite regularly:

Word based

Riddles: these are the classic word puzzles, whereby an everyday object is described in a cryptic manner - usually in the form of a verse.

Crossword clues: with or without the grid. You will normally be expected to derive the answer to the puzzle from the answers to these clues. Watch out for a common theme amongst the list of seemingly random words.

Extraction: normally presented in the form of a number of paragraphs, this method requires the selection of certain letters or words based on their position. Classic examples include first or last letters of each sentence.

Alternative alphabets

Braille: often, when the braille alphabet is used it will be disguised - mainly because there seem to be an infinite number of ways to do this. Hints towards this type of puzzle include references to "feeling" or "in the dark".

Semaphore: normally disguised using compass points or clock times, but any puzzle with eight possible "directions" could be semaphore. Hints normally involve reference to "waving" or "flags".

Morse/Binary: although very different in origin, these two methods are almost identical in the ways they are disguised as both comprise just two symbols. A common technique to make puzzles containing these methods is to remove the "spacing" between letters and, in the case of binary, any leading zeros.

Code Systems

Substitution: also referred to as "simple sub" or "crypto(gram)" this code is where each letter is replaced by a different letter.

Rot/Atbash: also referred to as "caesar cipher" or "rotation", the letters of the alphabet are shifted up or down a set number of places. Atbash (which may or may not be used in conjunction with rot) is where the alphabet is reversed so that A becomes Z, B becomes Y, etc.

Vigenere: slightly more tricky, but often used because a keyword is required to decode it. There are many decoders available online, and normally the main part of the puzzle is to work out the key. Where this is the case, there will normally be a hidden hint to it.

Comparison: this is more mathematics than cipher, but something to be considered when presented with a string of seemingly random letters. This is "decoded" by comparing the values of two or more adjacent letters.

Image based

"Say what you see" (or "swys") puzzles involve reading aloud a number of pictures to which (usually) fairly short names are attributed, thereby resulting in - hopefully - something which vaguely resembles a common phrase.

"Identify the pictures" (for want of a better name!): these puzzles work in much the same way as the "crossword clue" type (see above) puzzles. It is often possible to verify the name you have attributed to a particular picture by using a search engine to find images of that name.

Finally, not a type of puzzle but a tip: Puzzle writers will sometimes hide clues in the backgrounds of images (or any other large flat areas of colour). These can be found by loading the image into paint and flood-filling these areas with a different colour.

A much more comprehensive guide, together with some worked
examples, can be found in the Back to Basics section at Puzzletome.